Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006
Volume III. Invited Lectures
Editors
Marta Sanz-Solé
Universitat de Barcelona, SpainJavier Soria
Universitat de Barcelona, SpainJuan L. Varona
Universidad de La Rioja, Logroño, SpainJoan Verdera
Universitat Autónoma de Barcelona, Spain
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Note: The ICM2006 Proceedings are available only as a set, individual volumes cannot be ordered.
The International Congress of Mathematicians (ICM) is held every four years. It is a major scientific event, bringing together mathematicians from all over the world, and demonstrating the vital role that mathematics play in our society. In particular, the Fields Medals are awarded to recognize outstanding mathematical achievement. At the same time, the International Mathematical Union awards the Nevanlinna Prize for work in the field of theoretical computer science. The proceedings of ICM 2006, published as a three-volume set, present an overview of current research in all areas of mathematics and provide a permanent record the congress.
The first volume features the works of Fields Medallists and the Nevanlinna Prize winner, the plenary lectures, and the speeches and pictures of the opening and closing ceremonies and award sessions. The other two volumes present the invited lectures, arranged according to their mathematical subject.
pp. i–iv Front matterpp. v–x Contentspp. 1–26 Braids and differential equationsRobert Ghrist
pp. 27–55 Newton interpolation polynomials, discretization method, and certain prevalent properties in dynamical systemsAnton GorodetskiBrian HuntVadim Kaloshin
pp. 57–76 From combinatorics to ergodic theory and back againBryna Kra
pp. 77–98 From Brouwer theory to the study of homeomorphisms of surfacesPatrice Le Calvez
pp. 99–120 All, most, some differentiable dynamical systemsMichael Shub
pp. 121–146 Geodesics on flat surfacesAnton Zorich
pp. 147–155 Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems and relaxation approximationStefano Bianchini
pp. 156–182 Nonlinear Schrödinger equations in inhomogeneous media: wellposedness and illposedness of the Cauchy problemPatrick Gérard
pp. 183–201 The periodic Lorentz gas in the Boltzmann-Grad limitFrançois Golse
pp. 203–212 Conformal invariants and nonlinear elliptic equationsMatthew J. Gursky
pp. 213–227 Asymptotic solutions for large time of Hamilton–Jacobi equationsHitoshi Ishii
pp. 229–256 The weak-coupling limit of large classical and quantum systemsMario Pulvirenti
pp. 257–265 Symmetry of entire solutions for a class of semilinear elliptic equationsOvidiu Savin
pp. 267–290 Vortices in the Ginzburg–Landau model of superconductivitySylvia Serfaty
pp. 291–301 Recent developments in elliptic partial differential equations of Monge–Ampère typeNeil S. Trudinger
pp. 303–319 The initial value problem for nonlinear Schrödinger equationsLuis Vega
pp. 321–338 Singular solutions of partial differential equations modelling chemotactic aggregationJuan José L. Velazques
pp. 339–365 From topological field theory to deformation quantization and reductionAlberto S. Cattaneo
pp. 367–382 Matrix ansatz and large deviations of the density in exclusion processesBernard Derrida
pp. 383–408 Correlation functions of the Heisenberg spin chain: Bethe ansatz approachJean Michel Maillet
pp. 409–419 Gromov–Witten invariants and topological strings: a progress reportMarcos Mariño
pp. 421–442 The Cauchy problem in General RelativityIgor Rodnianski
pp. 443–458 Categorification and correlation functions in conformal field theoryJürgen FuchsChristoph SchweigertIngo Runkel
pp. 459–471 Soliton dynamics and scatteringAvy Soffer
pp. 473–498 Hypocoercive diffusion operatorsCédric Villani
pp. 499–518 Metastability: a potential theoretic approachAnton Bovier
pp. 519–533 On Ising dropletsRaphaël Cerf
pp. 535–558 Simple random covering, disconnection, late and favorite pointsAmir Dembo
pp. 559–574 Modelling genes: mathematical and statistical challenges in genomicsPeter Donnelly
pp. 575–594 Geometric stochastic analysis on path spacesK. David ElworthyXue-Mei Li
pp. 595–622 Statistical challenges with high dimensionality: feature selection in knowledge discoveryJianqing FanRunze Li
pp. 623–636 Random matrices and enumeration of mapsAlice Guionnet
pp. 637–647 The weak/strong survival transition on trees and nonamenable graphsSteven P. Lalley
pp. 649–667 New developments in stochastic dynamicsYves Le Jan
pp. 669–686 Stochastic classification modelsPeter McCullaghJie Yang
pp. 687–711 Random partitions and instanton countingAndrei Okounkov
pp. 713–739 Estimation in inverse problems and second-generation waveletsGérard KerkyacharianDominique Picard
pp. 741–762 Conformal restriction propertiesWendelin Werner
pp. 763–787 The complexity of generating functions for integer points in polyhedra and beyondAlexander Barvinok
pp. 789–826 Rational and algebraic series in combinatorial enumerationMireille Bousquet-Mélou
pp. 827–842 Towards a structure theory for matrices and matroidsJim GeelenBert GerardsGeoff Whittle
pp. 843–872 Cherednik algebras, Macdonald polynomials and combinatoricsMark Haiman
pp. 873–897 Poisson cloning model for random graphsJeong Han Kim
pp. 899–909 Randomness and regularityTomasz Łuczak
pp. 911–930 Additive combinatorics and geometry of numbersImre Z. Ruzsa
pp. 931–962 Geometric bistellar flips: the setting, the context and a constructionFrancisco Santos
pp. 963–984 A survey of Pfaffian orientations of graphsRobin Thomas
pp. 985–997 Determinant versus permanentManindra Agrawal
pp. 999–1018 The additivity problem in quantum information theoryAlexander S. Holevo
pp. 1019–1044 Complex networks and decentralized search algorithmsJon Kleinberg
pp. 1045–1069 On expander graphs and connectivity in small spaceOmer Reingold
pp. 1071–1094 Potential functions and the inefficiency of equilibriaTim Roughgarden
pp. 1095–1110 Sublinear time algorithmsRonitt Rubinfeld
pp. 1111–1136 Pseudorandomness and combinatorial constructionsLuca Trevisan
pp. 1137–1162 Least-squares finite element methodsPavel BochevMax Gunzburger
pp. 1163–1180 A posteriori error analysis and adaptive methods for partial differential equationsZhiming Chen
pp. 1181–1200 Error estimates for anisotropic finite elements and applicationsRicardo G. Durán
pp. 1201–1226 Linear subdivision schemes for the refinement of geometric objectsNira Dyn
pp. 1227–1253 Wave propagation software, computational science, and reproducible researchRandall J. LeVeque
pp. 1255–1270 Reduced basis method for the rapid and reliable solution of partial differential equationsYvon Maday
pp. 1271–1297 Finite element algorithms for transport-diffusion problems: stability, adaptivity, tractabilityEndre Süli
pp. 1299–1309 Ergodic control of diffusion processesVivek S. Borkar
pp. 1311–1319 Convex optimization of graph Laplacian eigenvaluesStephen Boyd
pp. 1321–1338 Controllability of evolution equations of fluid dynamicsOleg Yu. Emanouilov (Imanuvilov)
pp. 1339–1365 Port-Hamiltonian systems: an introductory surveyArjan van der Schaft
pp. 1367–1388 Passive linear discrete time-invariant systemsOlof J. Staffans
pp. 1389–1417 Control and numerical approximation of the wave and heat equationsEnrique Zuazua
pp. 1419–1432 Multiscale modeling for epitaxial growthRussel E. Caflisch
pp. 1433–1452 Compressive samplingEmmanuel J. Candès
pp. 1453–1472 Total variation based image denoising and restorationVicent Caselles
pp. 1473–1506 A wavelet based sparse grid method for the electronic Schrödinger equationMichael GriebelJan Hamaekers
pp. 1507–1522 Mathematical and numerical analysis for molecular simulation: accomplishments and challengesClaude Le Bris
pp. 1523–1540 Evolutionary dynamics of cooperationMartin A. Nowak
pp. 1599–1630 Understanding and misunderstanding the Third International Mathematics and Science Study: what is at stake and why K-12 education studies matterAlan Siegel
pp. 1541–1562 Fractional Brownian motion: stochastic calculus and applicationsDavid Nualart
pp. 1563–1582 Atomistic and continuum models for phase change dynamicsAnders Szepessy
pp. 1583–1598 Competitions and mathematics educationPetar S. Kenderov
pp. 1631–1644 Mathematics, the media, and the publicIan Stewart
pp. 1645–1661 Panel A — Controversial issues in K-12 mathematical educationpp. 1663–1672 Panel B — What are PISA and TIMSS? What do they tell us?pp. 1673–1696 Panel C — The role of mathematicians in K-12 mathematics educationpp. 1697–1718 On the origins of Hilbert’s sixth problem: physics and the empiricist approach to axiomatizationLeo Corry
pp. 1719–1742 Method versus calculus in Newton’s criticisms of Descartes and LeibnizNiccolo Guicciardini
pp. 1743–1768 e-learning mathematics